Work and Energy (part I):
Question: How do you raise an object?
Answer: Apply an upward force to it. The force must be at least as
large as the weight of the object.
more
force
applied
applied
force
applied
force
1 meter
 Weight
force
in order to lift box
Weight
less
force
applied
more
weight
1 meter
less
weight
Which one makes a louder “bang”
if dropped?
Obviously the big one……
Question: But what is the difference between lifting the box by
a height of, say 2 meters as opposed to 1 meters?
Answer: The force is the same in each case BUT:
(1) force is applied to the box over different amount of distance
(2) box makes louder “bang” when dropped on the floor
We say that the applied force does the WORK on the box:
Question: But what if we compare the process of lifting a “big” box to
that of lifting a “small” box?
Answer: Now the forces are different, it takes more force to lift a big
box than to lift a small box
Summary of our observations:
1) More WORK is done ON a system (the box) when a LARGER force
is applied to it.
2) More WORK is done ON the system when the force applied causes
the system to move through a larger distance
3) In order to do any work, applied force must be in the same direction
as motion
Work
Done
by
Force
Joules
=
The Force
Newtons
X
Distance
Moved
by
Force
Meters
Work
Done
by
Force
=
Joules
The Force
X
Newtons
Distance
Moved
by
Force
Meters
1 Joule = (1 Newton) X (1 meter)
1J=1NXm
W=FXd
F and d
Along the same line!!
TYPICAL VALUES FOR WORK!
quick-examples:
1) An 800 N person steps up onto a 1 meter tall stool, how much
work ? What force does this work?
force applied by legs
on body lifts the weight
of the person
1 meter
Work = W = 800N
force
of
lifting
X
1 meter
lift
NOTE : 1 joule = 0.239 cal  4186 J = 1 kcal
= 800 N X 1 m = 800 Joules
800 Joules = 191.2 calories
Work and Energy
2) You pull a box along the floor. How much work is done in moving
the box 10 m?
x = 10
x=0
20 Newtons
friction
10 meters
which force does the work?
The 20 N applied force!
W = (20N) X (10 m) = 200 Nm = 200 Joules
Work – Force Graphs: If we plot the Force that was applied to the
box as a function of distance we can find the total work done!
Force
20 N
The area under the
plot represents the
total Work done!!!!!
Area = length x height
= (10 m) x (20 N)
x = 10
= 200 Joules
Position
These graphs are great for more complex forces:
Force
10 N
Spring force
proportional to
the stretch
distance
What’s the work done from x =0
to x = 4m?
Area of a triangle is ½ base x height
= ½ (4 m) x (10 N) = 20 Joules!
x=4m
Position
Calculate the work done from
x =0 to x = 6 m.
Force
10 N
8N
3N
x = 1m
x = 3m
Position
x = 6m
When a force does work on an object it gives the object Energy of one form or another.
Energy is the ability to do work. But, what does this mean, really?
1
Now mass can do work
resulting in a flying monkey
2
do work on mass
work = mass x 10 m/s2
Mass
3
How? Drop it!
h = height of mass
Mass speeds up as it
falls
4
maximum speed
upon impact
h
Look at frame 2:
The mass CAN do work (but hasn’t) by virtue of its position or
“configuration”
Look at frame 4:
The mass CAN do work (but hasn’t) by virtue of its speed and impact
Energy
e.g.
The ABILITY to do WORK
A “raised” mass has the potential to pop a monkey
up into the air!
How to actually do the work is not the issue.
The issue is simply that “it” CAN.
Two types of energy:
1.
Kinetic Energy: energy by virtue of motion
2. Potential Energy: energy by virtue of
position (configuration
Forms of Energy
Kinetic (KE): energy by virtue
of motion
Potential (PE): energy by virtue
of position (configuration)
1.
1.
Translational
KE = ½ x mass x (speed)2
2. Rotational
3. Thermal
remember:
motion  temperature of
“atoms”
Gravitational
PE = (mass x 10 m/s2) x height
= Weight x height
2. Elastic (spring)
3. Chemical
4. Nuclear
5. Electromagnetic
Work Energy relationship
• Work = Force x Distance
– Work changes energy (work = change in energy)
– Energy increases when work is done on or to an object
– Energy decreases when work is done by an object
Spring
• Work is done to compress a spring a distance Dx.
• The change in the potential energy is identical to the work
done. W = DP.E.
P.E. = 1/2 k Dx2
k is the spring constant
(a characteristic of the spring)
• The spring can now do work on something else.
Potential Energy
• The motor pulls the cart up against gravity
WORK = Force x distance
mg x height
• Muscles do work against the tension in the bow string
• Muscles do work against gravity to lift the
axe above the ground
Potential Energy
• The roller coaster cart, the bow and the axe were all
given potential energy. The change in the potential energy
is identical to the work done.
W = DP.E.
• These objects now have the potential to do work and
convert that stored potential energy.
Kinetic Energy
• The energy associated with an objects motion.
K.E. = 1/2 m v2
m = mass
v = velocity
Without velocity, there is no KE
Chop, Chop
Law of Conservation of Energy (The 1st Law of Thermodynamics)
Energy is never created nor is it destroyed.
Energy can be transformed from type to type, BUT
When you add up all of the energy AFTER a process you will have
the exact same amount as BEFORE the process
Example Let’s look at the simple pendulum:
•The pendulum swings to and fro,
where it stops, conservation of energy
knows.
TOTAL ENERGY = Potential Energy +
Kinetic Energy
The Simple Pendulum
The total energy of this system is zero.
This simple pendulum could be the
sway in a grandfather clock,
a child on a swing,
a hypnotists watch, etc
Suppose someone does work against
gravity to give it some potential energy?
The Simple Pendulum
Suppose someone does work against
gravity to give it some potential energy?
The work done = Force x Distance
Force = m g
Distance = h
h
The work done = potential energy gained (DPE)
W =mgh
The total energy of the system is now (m g h), reflecting the
work done to the system.
To and Fro
To and Fro
To and Fro
To and Fro
To and Fro
To and Fro
To and Fro
To and Fro
The pendulum swings
until it has reached the
same height on the other
side, before pausing to
swing (oscillate) back.
h
Energy Exchange
When paused, the pendulum has its maximum
potential energy (mg h) and zero kinetic
energy. Total energy = mgh + 0
When at the bottom of its swing its height
is zero, therefore it has its minimum
potential energy (0) and its maximum
kinetic energy. It travels the fastest at the
bottom of its swing.
Total energy = 0 + 1/2 m v2
EVERYWHERE the TOTAL energy remains unchanged.
Energy Exchange
The energy sloshes from PE to KE and back again.
A pendulum weighing 5 kg is lifted against
gravity to a height of 2 m from its
equilibrium position. What is its speed at
the bottom of its swing?
Energy Exchange
The energy sloshes from PE to KE and back again.
A pendulum weighing 5 kg is lifted against
gravity to a height of 2 m from its
equilibrium position. What is its speed at
the bottom of its swing?
TOTAL Energy = PE + KE
= mg h + 0
= 5 kg 10 m/s2 2 m
= 100 Joules
Energy Exchange
At the bottom of its swing the total energy is still 100 Joules.
100 Joules = TOTAL Energy
= 0 + KE
= 1/2 m v2
= 1/2 5 kg v2
Energy Exchange
At the bottom of its swing the total energy is still 100 Joules.
100 Joules = TOTAL Energy
= 0 + KE
= 1/2 m v2
100 = 1/2 5 kg v2
2(100)/5 = v2
40 = v
6.3 m/s = velocity
Drum Roll Diver
The platform diver does work against
gravity by climbing the pole to the
platform at height h. This gives him
potential energy PE = mg h.
At the bottom, he is traveling the
maximum speed and has traded his
potential energy into the energy of
motion, kinetic energy.
TOTAL Energy is conserved at every
point along the way!
Drum Roll Diver
If the idiot climbed to a height
of 20 meters, how much is his mass?
PE = 10,000 = mg h
Drum Roll Diver
If the idiot climbed to a height
of 20 meters, how much is his mass?
PE = 10,000 = mg h
m = 10,000/gh = 10,000/10(20)
= 50 kg
The Curved Track:
Q1: How did the ball get to the “starting position” in the first place?
Q2: What forms of energy does the ball possess at each point of its
journey? Where did it get the energy?
The Curved Track:
“Ideal Case”: no friction, no rolling
no sound
no air resistance
“Real Case”:friction
sound
air resistance, etc.
The Curved Track:
Some of the energy appears to be “lost” in the transfer. Where does
it go?
In the track example.
Reversible Part:
some of……
gravitational PE  rotational KE  gravitational PE
translational KE
Irreversible Part:
Remainder of
gravitational PE
Thermal (friction)
Sound
lost to the surroundings
By building a curved track, we can get some of the energy back…..
but never all of it. The ball gives up its gravitational energy not only
to rotational and translational kinetic forms but also to thermal
forms and to sound (another example of translational Kinetic)
Point: We can “get back” the ordinary rotational and translational KE
We cannot “get back” the thermal, sounds, etc…
Actual Efficiency (AE) of a process: “what percentage of the INPUT
produces useful OUTPUT”
 Useful Energy OUTPUT
AE  
 Total Energy INPUT

  100%


Or, since POWER is the rate of energy flow (or work performance)
 Useful Power OUTPUT
AE  
 Total Power INPUT

  100%


Example
Lift a 2 kg brick to height of 2 meters. Drop it and do 15 Joules
of work in driving a nail. What is this processes actual efficiency?
 Useful Energy OUTPUT
AE  
 Total Energy INPUT

  100%




 15 Joules
15 Joules


AE  
 100%  

40 Joules
 2 kg  10 m 2  2 m 

s



  100%  37.5%


The energy (or Power) which is NOT converted to a useful form is called
exhaust for the process…..
Common Examples:
Thermal Energy Output (friction, air resistance, etc.)
Sound (friction, collisions)
Light (friction, “dissipative atomic processes
Example continued:
The brick does 15 Joules of useful work, thus the process has an
exhaust of
40 Joules – 15 Joules = 25 Joules
input
useful
output
scattered, non-useful
output [thermal, sound, etc.]